Index Analysis
DAEs are no ODEs. Actually, Differential agebraic equations (DAEs) are a mixture of ordinary differential equations (ODEs) and algebraic relations. This may create difficulties, which are not seen at the first sight. The analysis shows that due this mixture hidden differentiation might occur. Recalling from analysis that differentiation is not an unbounded operator, such a process is much more difficult to handle than the integrals used for solving ODEs. E.g. imagine a sinosoidal signal of small amplitude but with high frequency, such as a numerical error, the derivative is of much larger magnitude.
Clearly, the more derivatives involved in the exact solution of a DAE, the more one needs to be careful in numerical computations. The index is a measure for this difficutly. That is why it is important to know the index before simulation.
Group members working on that field
- Andreas Bartel
- Michael Günther
Cooperations
- Giuseppe Ali (Academia)
- Sascha Baumanns (Academia)
- Caren Tischendorf (Academia)
Publications
- 1997
692.
Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its \(^{1}\)B\(_{2}\) electronic state
Molecular Physics, 91 (4) :653-662
1997691.
Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its \(^{1}\)B\(_{2}\) electronic state
Molecular Physics, 91 (4) :653-662
1997690.
Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its 1B2 electronic state
Molecular Physics, 91 (4) :653-662
1997689.
Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X\verb=~= \(^{3}\)B\(_{1}\) State of Methylene CH\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press688.
Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X\verb=~= \(^{3}\)B\(_{1}\) State of Methylene CH\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press687.
Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X~ 3B1 State of Methylene CH2
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press686.
Klamroth, Kathrin; Mengersen, Ingrid
The Ramsey number r(K_1,3,C_4,K_4)
Utilitas Mathematica, 52 :65-81
1997685.
Jensen, Per; Sauer, Stephan P. A.
Theoretical calculations of the hyperfine structure in the spectra of H\(_{3}\)\(^{+}\) and its deuterated isotopomers
Molecular Physics, 91 (2) :319-332
1997684.
Jensen, Per; Sauer, Stephan P. A.
Theoretical calculations of the hyperfine structure in the spectra of H\(_{3}\)\(^{+}\) and its deuterated isotopomers
Molecular Physics, 91 (2) :319-332
1997683.
Jensen, Per; Sauer, Stephan P. A.
Theoretical calculations of the hyperfine structure in the spectra of H3+ and its deuterated isotopomers
Molecular Physics, 91 (2) :319-332
1997682.
Jensen, Per
Theoretical Rotation-Vibration Energies of X\verb=~=\(^{3}\)B\(_{1}\) NH\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 181 (1) :207-214
1997
Herausgeber: Academic Press681.
Jensen, Per
Theoretical Rotation-Vibration Energies of X\verb=~=\(^{3}\)B\(_{1}\) NH\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 181 (1) :207-214
1997
Herausgeber: Academic Press680.
Jensen, Per
Theoretical Rotation-Vibration Energies of X~3B1 NH2+
Journal of Molecular Spectroscopy, 181 (1) :207-214
1997
Herausgeber: Academic Press- 1996
679.
Kukui, A.; Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
A Gaskinetic Investigation of HOBr Reactions with Cl(\(^{2}\)P), O(\(^{3}\)P) and OH(\(^{2}\)\(\Pi\)). The Reaction of BrCl with OH(\(^{2}\)\(\Pi\))
Berichte der Bunsengesellschaft für physikalische Chemie, 100 (4) :455-461
1996678.
Kukui, A.; Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
A Gaskinetic Investigation of HOBr Reactions with Cl(\(^{2}\)P), O(\(^{3}\)P) and OH(\(^{2}\)\(\Pi\)). The Reaction of BrCl with OH(\(^{2}\)\(\Pi\))
Berichte der Bunsengesellschaft für physikalische Chemie, 100 (4) :455-461
1996677.
Kukui, A.; Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
A Gaskinetic Investigation of HOBr Reactions with Cl(2P), O(3P) and OH(2Π). The Reaction of BrCl with OH(2Π)
Berichte der Bunsengesellschaft für physikalische Chemie, 100 (4) :455-461
1996676.
Gu, Jian-ping; Buenker, Robert J.; Hirsch, Gerhard; Jensen, Per; Bunker, Philip R.
An ab Initio Calculation of BH\(_{2}\)\(^{-}\) Rovibronic Energies: A Very Small Singlet-Triplet Splitting
Journal of Molecular Spectroscopy, 178 (2) :172-183
1996
Herausgeber: Academic Press675.
Gu, Jian-ping; Buenker, Robert J.; Hirsch, Gerhard; Jensen, Per; Bunker, Philip R.
An ab Initio Calculation of BH\(_{2}\)\(^{-}\) Rovibronic Energies: A Very Small Singlet-Triplet Splitting
Journal of Molecular Spectroscopy, 178 (2) :172-183
1996
Herausgeber: Academic Press674.
Gu, Jian-ping; Buenker, Robert J.; Hirsch, Gerhard; Jensen, Per; Bunker, Philip R.
An ab Initio Calculation of BH2- Rovibronic Energies: A Very Small Singlet-Triplet Splitting
Journal of Molecular Spectroscopy, 178 (2) :172-183
1996
Herausgeber: Academic Press673.
Kolbuszewski, M.; Bunker, Philip R.; Kraemer, Wolfgang P.; Osmann, Gerald; Jensen, Per
An ab initio calculation of the rovibronic energies of the BH\(_{2}\) molecule
Molecular Physics, 88 (1) :105-124
1996672.
Kolbuszewski, M.; Bunker, Philip R.; Kraemer, Wolfgang P.; Osmann, Gerald; Jensen, Per
An ab initio calculation of the rovibronic energies of the BH\(_{2}\) molecule
Molecular Physics, 88 (1) :105-124
1996671.
Kolbuszewski, M.; Bunker, Philip R.; Kraemer, Wolfgang P.; Osmann, Gerald; Jensen, Per
An ab initio calculation of the rovibronic energies of the BH2 molecule
Molecular Physics, 88 (1) :105-124
1996670.
Jacob, Birgit
Destabilization of infinite-dimensional time-varying systems via dynamical output feedback
, Recent developments in operator theory and its applications (<prt>W</prt>innipeg, <prt>MB</prt>, 1994) Band 87 aus Oper. Theory Adv. Appl.
Seite 193--206
Herausgeber: Birkhäuser, Basel
1996
193--206669.
Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Emission of nitrous oxide and methane from aero engines: Monitoring by tunable diode laser spectroscopy
Infrared Physics and Technology, 37 (1) :75-81
1996
Herausgeber: Pergamon668.
Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Emission of nitrous oxide and methane from aero engines: Monitoring by tunable diode laser spectroscopy
Infrared Physics and Technology, 37 (1) :75-81
1996
Herausgeber: Pergamon
